# Return the desired percentiles plus the geometric mean
bp.vals <- function(x, probs=c(.05, 0.25, 0.5, 0.75, .95), width=0.8) {
  r <- quantile(x, probs=probs , na.rm=TRUE)
  r <- c(r, width)
  names(r) <- c("ymin", "lower", "middle", "upper", "ymax", "width")
  r
}

\(I_o\) for all itineraries

ggplot(data = user_itineraries_complete, 
       aes(x = trip_length_bucket, 
           y = io)) +
    stat_summary(fun.data = bp.vals, geom = "boxplot", fill ="#fc8d62") +
    scale_y_log10(breaks = c(1:5)) +
    coord_flip() +
    xlab(expression(paste("d"[o], "(u) in mins"))) +
    ylab(expression(paste("User choice inefficiency (i"[o], ")"))) +
    guides(fill = FALSE)
ggsave("io-for-all.pdf", width = 5, height = 2.2)

Overall, longer itineraries tend to incurr in higher inefficiencies. For 20-30min itineraries, more than half have no inefficiency. For 40-50 min itineraries, half of the itineraries have an inefficiency of 1.6 or higher. For a 45 mins itinerary, \(i_o = 1.6\) implies there was an 28-min alterantive.

\(i_s\) for all \(i_c\)

ggplot(data = user_itineraries_complete, 
       aes(x = trip_length_bucket, 
           y = is)) +
    stat_summary(fun.data = bp.vals, geom = "boxplot", fill ="#7DBBC3") +
    scale_y_log10(breaks = c(1, 1.2, 1.4)) +
    coord_flip() +
    xlab(expression(paste("d"[o], "(u) in mins"))) +
    ylab(expression(paste("System operation inefficiency (i"[s], ")"))) +
    guides(fill = FALSE)
ggsave("is-for-all.pdf", width = 5, height = 2.2)

Contrary to what is experienced by user, system efficiency is concentrated on shorter itineraries. For 40-50-min itineraries, over 75% of all itineraries have no inefficiency.

It seems that most inefficiency in longer itineraries experienced by users is not due to system operation inefficiency.

Considering \(i_c\)

How often do users choose the best itinerary according to the schedule?

user_itineraries_complete %>% 
    group_by(trip_length_bucket) %>% 
    select(ic) %>% 
    summarise(best = sum(ic == 0, na.rm = T) / sum(!is.na(ic)), 
              n = sum(!is.na(ic))) 
Adding missing grouping variables: `trip_length_bucket`

Most of the time we can identify which trip from the schedule a user took, the user took the best according to the schedule. This happens 85-89% of the itineraries, depending on their duration.

Did the schedule happen faithfully when the user followed it?

user_itineraries_complete %>% 
    group_by(trip_length_bucket) %>% 
    filter(!is.na(ic), ic == 0) %>% 
    ggplot(aes(x = trip_length_bucket, 
               y = is)) +
    stat_summary(fun.data = bp.vals, geom = "boxplot", fill ="#7DBBC3") +
    # scale_y_log10() +
    coord_flip() +
    xlab(expression(paste("d"[o], "(u) in mins"))) +
    ylab(expression(paste("System operation inefficiency (i"[s], ")"))) +
    guides(fill = FALSE)

     
user_itineraries_complete %>% 
    group_by(trip_length_bucket) %>% 
    filter(!is.na(ic), ic == 0) %>% 
    ggplot(aes(x = trip_length_bucket, 
               y = io)) +
    stat_summary(fun.data = bp.vals, geom = "boxplot", fill ="#fc8d62") +
    scale_y_log10(breaks = c(1, 1.1, 1.2, 1.3)) +
    coord_flip() +
    xlab(expression(paste("d"[o], "(u) in mins"))) +
    ylab(expression(paste("User choice inefficiency (i"[o], ")"))) +
    guides(fill = FALSE)
ggsave("io-for-ic_eq_zero.pdf", width = 5, height = 2.2)

Following the schedule in general leads users to a low inefficiency (\(i_o = 1\) for 66-80% of the itineraries) longer itineraries tend to have have lower inefficinecy.

\(i_c > 0\)

$i_c > 0 $

plotly::ggplotly(p)
We recommend that you use the dev version of ggplot2 with `ggplotly()`
Install it with: `devtools::install_github('hadley/ggplot2')`

When the user deviates from the itinerary recommended by the schedule, the user outperforms the choice proposed by the schedule a significant proportion of the time.

---
title: "Paper stories"
output: html_notebook
---

```{r, echo=FALSE, message=FALSE}
library(tidyverse)
library(lubridate)

theme_set(theme_bw())

all_itineraries <- read_csv("data/all_itineraries_metrics-v2.csv",
                            col_types = cols(
                              .default = col_double(),
                              date = col_date(format = ""),
                              user_trip_id = col_character(),
                              itinerary_id = col_integer(),
                              planned_start_time = col_datetime(format = ""),
                              actual_start_time = col_datetime(format = ""),
                              exec_start_time = col_datetime(format = ""),
                              trip_length_bucket = col_character(),
                              hour_of_day = col_integer(),
                              period_of_day = col_character(),
                              weekday = col_character(),
                              day_type = col_character(),
                              itinerary_id_fo = col_integer(),
                              itinerary_id_fs = col_integer()
                            )) %>%
  filter(date != ymd("2017-05-10")) %>%
    mutate(period_of_day = factor(
        period_of_day,
        ordered = TRUE,
        levels = c(
        "early_morning",
        "morning",
        "midday",
        "afternoon",
        "evening",
        "night"
        )
        ))
        
user_itineraries_complete <- all_itineraries %>%
    filter(trip_length_bucket != "50+") %>% 
    group_by(date, user_trip_id) %>%
    arrange(itinerary_id) %>% 
    slice(1)

user_itineraries_with_plans <- all_itineraries %>%
  filter(itinerary_id == "0", !is.na(planned_duration_mins))

```

```{r}
# Return the desired percentiles plus the geometric mean
bp.vals <- function(x, probs=c(.05, 0.25, 0.5, 0.75, .95), width=0.8) {
  r <- quantile(x, probs=probs , na.rm=TRUE)
  r <- c(r, width)
  names(r) <- c("ymin", "lower", "middle", "upper", "ymax", "width")
  r
}
```

## $I_o$ for all itineraries


```{r}
user_itineraries_complete %>% 
    group_by(trip_length_bucket) %>% 
    summarise(median(io), median(is), sum(io == 1) / n(), sum(is == 1) / n())
```


```{r}
ggplot(data = user_itineraries_complete, 
       aes(x = trip_length_bucket, 
           y = io)) +
    stat_summary(fun.data = bp.vals, geom = "boxplot", fill ="#fc8d62") +
    scale_y_log10(breaks = c(1:5)) +
    coord_flip() +
    xlab(expression(paste("d"[o], "(u) in mins"))) +
    ylab(expression(paste("User choice inefficiency (i"[o], ")"))) +
    guides(fill = FALSE)
ggsave("io-for-all.pdf", width = 5, height = 2.2)
```

Overall, longer itineraries tend to incurr in higher inefficiencies. For 20-30min itineraries, more than half have no inefficiency. For 40-50 min itineraries, half of the itineraries have an inefficiency of 1.6 or higher. For a 45 mins itinerary, $i_o = 1.6$ implies there was an 28-min alterantive.

## $i_s$ for all $i_c$

```{r}
ggplot(data = user_itineraries_complete, 
       aes(x = trip_length_bucket, 
           y = is)) +
    stat_summary(fun.data = bp.vals, geom = "boxplot", fill ="#7DBBC3") +
    scale_y_log10(breaks = c(1, 1.2, 1.4)) +
    coord_flip() +
    xlab(expression(paste("d"[o], "(u) in mins"))) +
    ylab(expression(paste("System operation inefficiency (i"[s], ")"))) +
    guides(fill = FALSE)
ggsave("is-for-all.pdf", width = 5, height = 2.2)

```

Contrary to what is experienced by user, system efficiency is concentrated on shorter itineraries. For 40-50-min itineraries, over 75\% of all itineraries have no inefficiency.

It seems that most inefficiency in longer itineraries experienced by users is not due to system operation inefficiency. 

## Considering $i_c$

How often do users choose the best itinerary according to the schedule? 


```{r}
user_itineraries_complete %>% 
    group_by(trip_length_bucket) %>% 
    select(ic) %>% 
    summarise(best = sum(ic == 0, na.rm = T) / sum(!is.na(ic)), 
              n = sum(!is.na(ic))) 

```

Most of the time we can identify which trip from the schedule a user took, the user took the best according to the schedule. This happens 85-89% of the itineraries, depending on their duration.


### Did the schedule happen faithfully when the user followed it?

```{r}
user_itineraries_complete %>% 
    group_by(trip_length_bucket) %>% 
    filter(!is.na(ic), ic == 0) %>% 
    ggplot(aes(x = trip_length_bucket, 
               y = is)) +
    stat_summary(fun.data = bp.vals, geom = "boxplot", fill ="#7DBBC3") +
    # scale_y_log10() +
    coord_flip() +
    xlab(expression(paste("d"[o], "(u) in mins"))) +
    ylab(expression(paste("System operation inefficiency (i"[s], ")"))) +
    guides(fill = FALSE)
     
user_itineraries_complete %>% 
    group_by(trip_length_bucket) %>% 
    filter(!is.na(ic), ic == 0) %>% 
    ggplot(aes(x = trip_length_bucket, 
               y = io)) +
    stat_summary(fun.data = bp.vals, geom = "boxplot", fill ="#fc8d62") +
    scale_y_log10(breaks = c(1, 1.1, 1.2, 1.3)) +
    coord_flip() +
    xlab(expression(paste("d"[o], "(u) in mins"))) +
    ylab(expression(paste("User choice inefficiency (i"[o], ")"))) +
    guides(fill = FALSE)
ggsave("io-for-ic_eq_zero.pdf", width = 5, height = 2.2)

```

Following the schedule in general leads users to a low inefficiency ($i_o = 1$ for 66-80% of the itineraries) longer itineraries tend to have have lower inefficinecy.

```{r}
user_itineraries_complete %>% 
    group_by(trip_length_bucket) %>% 
    filter(!is.na(ic), ic == 0) %>% 
    summarise(went_bad = sum(io == 1) / n())
```


### $i_c > 0$

*$i_c > 0 $*

```{r}
user_itineraries_complete %>% 
    group_by(trip_length_bucket) %>% 
    filter(!is.na(ic), ic > 0) %>% 
    mutate(situation = case_when(
        is > 1 & io == 1 ~ "Deviation was better",
        is == 1 & io > 1 ~ "Schedule was better", 
        TRUE ~ "Compound"
    ) %>% factor(levels = c("Schedule was better", "Compound", "Deviation was better"), ordered = T)
    ) %>% 
    ggplot(aes(x = trip_length_bucket, fill = situation)) +
    geom_bar(position = "fill") + 
    scale_fill_brewer(type = "qual") + 
    labs(x = expression(paste("d"[o], "(u) in mins")), 
         y = "Proportion") + 
    theme(legend.position = "bottom", legend.title = element_blank()) + 
    coord_flip()
ggsave("situations-ic_gt_zero.pdf", width = 5, height = 2.5)

```

When the user deviates from the itinerary recommended by the schedule, the user outperforms the choice proposed by the schedule a significant proportion of the time. 

